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[a,b]-factorization of a graph

✍ Scribed by Mikio Kano

Publisher: John Wiley and Sons
Year: 1985
Tongue: English
Weight: 781 KB
Volume: 9
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190090111

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✦ Synopsis

Let a and b be integers such that 0 s a s b. Then a graph G is called an [a,bl-graph if a 6 dG(x) s b for every x E V(G), and an [a,b]-factor of a graph is defined to be its spanning subgraph F such that a d dF(x) d b for every vertex x, where dG(x) and dJx) denote the degrees of x in G and F, respectively. If the edges of a graph can be decomposed into [a,bl-factors then w e say that the graph is [a,b]-factorable. We prove the following two theorems: (i) a graph G is [2a,2b]-factorabIe if and only if G is a [2arn,2brn]-graph for some integer rn, and (ii) every (8rn + 2k, lorn + 2kl-graph is [1,2]-factorable.

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